Interior Hölder continuity of solutions of non-degenerate parabolic equations is well-understood.
Moser adapted the techniques of DeGiorgi for uniformly elliptic linear equations for uniformly parabolic linear equations by studying the oscillation of solutions in a family of shrinking space-time cylinders reflecting the scaling invariance of the equation, see [1]}, [2]}.
These methods where subsequently generalized by Ladyženskaja, Solonnikov and Ural'ceva for quasi-linear non-degenerate parabolic equations, see [3]}.
